Resonator circuits, also denoted as tank circuits, are widely used as frequency selective elements in a variety of radio frequency components, such as filters, amplifiers, and oscillators. Typically, resonator circuits comprise inductors and capacitors, wherein the inductors and capacitors are connected to be in resonance at a specific resonance frequency. The quality of resonator circuits is thereby characterized by a quality factor. The characteristics of resonator circuits are of major interest in the design of radio frequency oscillators, in particular when implemented as radio frequency integrated circuits (RFICs) on semiconductor substrates. In particular, the response of the resonator circuits with regard to leakage currents or currents at harmonic frequencies can have a major impact on the frequency stability and phase noise performance of the radio frequency oscillators.
Common resonator circuits exhibit a resistive characteristic when excited at the resonance frequency, and a capacitive characteristic when excited at frequencies above the resonance frequency. Consequently, higher order current components in conjunction with the Groszkowski effect may lead to reduced frequency stability and increased flicker noise up-conversion, i.e. reduced close-in phase noise performance, of radio frequency oscillators.
For improving the phase noise performance of radio frequency oscillators, noise filtering techniques are applied. These techniques rely on interposing a further resonator circuit having a resonance frequency at 2ω0 in a common source of the transistors, e.g. core transistors. These techniques, however, use an additional tunable inductor and increase the die area on the semiconductor substrate.
For reducing an amount of higher order drain current harmonics, resistors are added in series with the sources of the transistors for linearizing the operation of the transistors. However, the radio frequency oscillator start-up margin is usually reduced.
By adding resistors in series with the drain of the transistors, the resistance in conjunction with a parasitic drain capacitance can introduce a delay in a loop gain for shifting both an impulse sensitivity function (ISF) and a current waveform of the radio frequency oscillators. Flicker noise up-conversion is reduced by specifically tailoring the component values. However, the phase noise performance in the 20 dB/decade region is degraded particularly at low supply voltages and high current consumptions.
In J. Groszkowski, “The interdependence of frequency variation and harmonic content, and the problem of constant-frequency oscillators,” Proc. IRE, vol. 21, no. 7, pp. 958-981, July 1934, the Groszkowski effect is studied.
In M. Babaie and R. B. Staszewski, “A class-F CMOS oscillator,” IEEE JSSC, vol. 48, no. 12, pp. 3120-3133, December 2013, a resonator circuit and a radio frequency oscillator are described.